Algebra Introduction

This is about a Introduction to Algebra.

The basics of algebra include numbers, variables, constants, expressions, equations, linear equations, quadratic equations. Further, it involves the basic arithmetic operations of addition, subtraction, multiplication, and division within the algebraic expressions.

We work with numbers in arithmetic, while in algebra we use numbers as well as Alphabets such as $A, B, C, a, b$, and $c$ for any numerical values we choose. We can say that algebra is an extension of arithmetic. For example, the arithmetic sum of two numbers $5+3=8$ means that the sum of numbers 5 and 3 is 8. In algebra, two numbers can be summed by the expression $ x+y=z$ which is the general form that can be used to add any two numbers. For example, if $x=5$ and $y=3$ then $x+y$ will be equivalent to the left-hand side ($5+3$) and the summation of these numbers will be equivalent to the right-hand side $z$ which is 8.

In algebra all arithmetic operators such as $+, -, \times, =$ and $\div$ etc., can be use used.

For example, $x-y=z$ means that the difference between two numbers is equal to the number represented by the letter z. In algebra, many other notations used are exactly the same as in arithmetic. For example,

$c=a\times b$ means that the product of two numbers represented by $a$ and $b$ is equal to the number $c$.

$x \times x \times x$ can be written as $a^4$.

Algebra Introduction

From the above discussion, note that letters of alphabets represent variable,s and arithmetic operator (+, -, etc) represents the mathematical operation on a variable. The combination of numbers and letters of alphabets is called an algebraic expression. For example, $8x + 7y$, $x+y$ and $7x^2+2xy-5y^2$ etc., are examples of expression.

Some important points to remember:

  • A variable is a quantity (usually denoted by letters of the alphabet) in algebraic expressions and equations, that changes from place to place, person, to person, and/or time to time. The variable can have any one of a range of possible values.
  • A factor that multiplies with a variable. For example, in $2x^3+3x=0$, $x$ is a variable, 2 is coefficient of $x^3$ and 3 is coefficient of $x$.

That’s all about algebra introduction.